Bicycle hydraulic operating devices, e.g. brake operating devices for hydraulic braking systems, typically include a master cylinder, reservoir, and handlebar clamp. In some prior hydraulic operating devices the axes of the reservoir, master cylinder, and handlebar clamp are arranged in a common plane. It may be desirable to bleed the reservoir to remove gas in the hydraulic braking system. However, when the axes of the reservoir, master cylinder, and handlebar clamp are arranged in a common plane is it difficult to bleed the reservoir when the bicycle is in an upright riding position.